LEADER 05301nam 22007695 450 001 9910409990403321 005 20250610110441.0 010 $a3-030-48408-4 024 7 $a10.1007/978-3-030-48408-8 035 $a(CKB)4100000011325746 035 $a(MiAaPQ)EBC6237411 035 $a(DE-He213)978-3-030-48408-8 035 $a(PPN)248596926 035 $a(MiAaPQ)EBC30174232 035 $a(EXLCZ)994100000011325746 100 $a20200625d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProbability and Stochastic Processes for Physicists /$fby Nicola Cufaro Petroni 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (xiii, 373 pages) $cillustrations 225 1 $aUNITEXT for Physics,$x2198-7882 311 08$a3-030-48407-6 327 $aPart 1: Probability -- Chapter 1. Probability spaces -- Chapter 2. Distributions -- Chapter 3. Random variables -- Chapter 4. Limit theorems -- Part 2: Stochastic Processes -- Chapter 5. General notions -- Chapter 6. Heuristic de?nitions -- Chapter 7. Markovianity -- Chapter 8. An outline of stochastic calculus -- Part 3: Physical modeling -- Chapter 9. Dynamical theory of Brownian motion -- Chapter 10. Stochastic mechanics -- Part 4: Appendices -- A Consistency (Sect. 2.3.4) -- B Inequalities (Sect. 3.3.2) -- C Bertrand?s paradox (Sect. 3.5.1) -- D Lp spaces of rv?s (Sect. 4.1) -- E Moments and cumulants (Sect. 4.2.1) -- F Binomial limit theorems (Sect. 4.3) -- G Non uniform point processes (Sect 6.1.1) -- H Stochastic calculus paradoxes (Sect. 6.4.2) -- I Pseudo-Markovian processes (Sect. 7.1.2) -- J Fractional Brownian motion (Sect. 7.1.10) -- K Ornstein-Uhlenbeck equations (Sect. 7.2.4) -- L Stratonovich integral (Sect. 8.2.2) -- M Stochastic bridges (Sect. 10.2) -- N Kinematics of Gaussian di?usions (Sect. 10.3.1) -- O Substantial operators (Sect. 10.3.3) -- P Constant di?usion coe?cients (Sect. 10.4). 330 $aThis book seeks to bridge the gap between the parlance, the models, and even the notations used by physicists and those used by mathematicians when it comes to the topic of probability and stochastic processes. The opening four chapters elucidate the basic concepts of probability, including probability spaces and measures, random variables, and limit theorems. Here, the focus is mainly on models and ideas rather than the mathematical tools. The discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes, including, for example, stationarity and ergodicity, Poisson and Wiener processes and their trajectories, other Markov processes, jump-diffusion processes, stochastic calculus, and stochastic differential equations. All these conceptual tools then converge in a dynamical theory of Brownian motion that compares the Einstein?Smoluchowski and Ornstein?Uhlenbeck approaches, highlighting the most important ideas that finally led to a connection between the Schrödinger equation and diffusion processes along the lines of Nelson?s stochastic mechanics. A series of appendices cover particular details and calculations, and offer concise treatments of particular thought-provoking topics. 410 0$aUNITEXT for Physics,$x2198-7882 606 $aPhysics 606 $aProbabilities 606 $aMathematical physics 606 $aDynamics 606 $aErgodic theory 606 $aVibration 606 $aDynamics 606 $aQuantum theory 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 615 0$aPhysics. 615 0$aProbabilities. 615 0$aMathematical physics. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aVibration. 615 0$aDynamics. 615 0$aQuantum theory. 615 14$aMathematical Methods in Physics. 615 24$aProbability Theory and Stochastic Processes. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aVibration, Dynamical Systems, Control. 615 24$aQuantum Physics. 676 $a530.13 700 $aCufaro Petroni$b Nicola$4aut$4http://id.loc.gov/vocabulary/relators/aut$0535910 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910409990403321 996 $aProbability and Stochastic Processes for Physicists$91882347 997 $aUNINA